The obligation to financially support your child does not end after divorce. In that sense, both parents are responsible for providing child support in Texas. However, actual support payments from one parent to the other are generally mandatory if one parent has more overnights with the child under a custody arrangement.
Right to Support
In Texas, you are presumed to be financially supporting any child currently living with you. If one parent has more overnights with the child than the other parent, she is referred to as the custodial parent and is generally entitled to support payments from the other, noncustodial, parent. In cases where both parents' time with the child is equal and both have similar incomes, a court could conclude that no payments need to be made. However, this does not relieve you of your responsibility to financially support the child while he is in your care.